A simulation of the Schwinger model in the overlap formalism

TL;DR

This paper demonstrates that a lattice simulation of the massless Schwinger model using the overlap formalism accurately reproduces the axial symmetry breaking and fermion condensate, highlighting the role of topological charge.

Contribution

It introduces a lattice formulation with overlap fermions that explicitly captures the axial symmetry breaking due to topological charge in the Schwinger model.

Findings

Monte Carlo simulation confirms the correct fermion condensate value.

Fermion condensate originates from topological charge sector one.

The overlap formalism effectively reproduces continuum symmetry breaking.

Abstract

In the continuum, the single flavor massless Schwinger model has an exact global axial $U(1)$ symmetry in the sector of perturbative gauge fields. This symmetry is explicitly broken by gauge fields with nonzero topological charge inducing a nonzero expectation value for the bilinear $\bar\psi\psi$. We show that a lattice formulation of this model, using the overlap formalism to treat the massless fermions, explicitly exhibits this phenomenon. A Monte Carlo simulation of the complete system yields the correct value of the fermion condensate and shows unambiguously that it originates from the sector of topological charge equal to unity.